Electric field due to a nonconducting sphere

[cesaruelas]

Homework Statement

A spherical nonconducting surface of radius R is uniformly charged in its surface with net charge +Q. Calculate the electric field at a point P which is located at a distance R from the right border of the sphere. Calculate the electric field at a point R/2 at each side of the center of the sphere.

Homework Equations

I came up with this.
Let p=Q/V
dq = pdV
V = f(x,y,z) = x^2 + y^2 + z^2 - R = 0
∂V = 2y∂y
and E^→_p = k_e ∫^2R_-R dq/y^2 r^→

The Attempt at a Solution

After integration, E^→_p = 2k_eQ(ln2)/R r^→

My question is, am I applying the concept of electric field due to a charge distribution in the correct way? I think I might have got it wrong with the dV component... Also, since the topic is Gauss Law, how am I supposed to use the concept of a gaussian surface to calculate electric field?

 

[cesaruelas]

My other attempt would be to construct a gaussian surface enclosing this sphere and express the electric field at p as Q/epsilon*(4*pi*R^2) which would come to kQ/R^2 (same as if i had taken it to be a point charge). THIS... IS... CONFUSING!